After doing some googling the problem was found, as it seems, and it is not on either developers, Kaspersky or my side. My network provider inserts the banner ad via the jscript insertion, Kaspersky notices it (as I said, it does its main job pretty well) and blocks the source of those ads, blocking the connection and thus preventing loading of the rewards/shop page itself.
I apologize for my misunderstanding, I was wrong.